When trying to solve a pde using Laplace transform, I need to invert an expression of the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\exp{(-as-b\sqrt{s})}}{s^2}[/tex]

A friend told me that Mathematica cannot invert such expression. I try using convolution but a bit loss when trying to evaluate the integral of Erfc(.).

[tex]L^{-1}\{\frac{\exp{(-as-b\sqrt{s})}}{s^2} \}[/tex]

[tex]=L^{-1} \{ \frac{e^{-as}}{s} \} * L^{-1} \{ \frac{e^{-b\sqrt{s}}}{s} \} [/tex]

[tex]=H(t-a) * Erfc(\frac{b}{2\sqrt{t}}\) [/tex]

[tex]=\int_0^t H(t-\tau-a) Erfc(\frac{b}{2\sqrt{\tau}}\) d\tau[/tex]

How do we proceed from here?

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# Laplace Inversion

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